The strong solution of the Monge–Ampère equation on the Wiener space for log-concave densities

Let (W,H,μ) be an abstract Wiener space, assume that $\text{d}\text{ν=L}\text{d}\text{μ}$ is a second probability measures on $\text{(W,}\text{B}\text{(W))}$ such that $\text{L=}\text{1}\text{c}\text{exp}\text{?f}$, with $\text{f∈}\text{D}{}_{\mathrm{2,1}}$ lower bounded and H-convex. Let $\text{T=I}{}_{\mathrm{W}}\text{+??,}\text{?∈}\text{D}{}_{\mathrm{2,1}}$, be the solution of the Monge problem transporting μ to ν and realizing the H-Wasserstein distance between μ and ν. We prove that $\text{?∈}\text{D}{}_{\mathrm{2,2}}$ hence the Gaussian Jacobian $\text{Λ=}\text{det}{}_2\text{(I+?}{}^2\text{?)}\text{exp}\text{{}\text{L}\text{??1/2|??|}{}_{\mathrm{H}}{}^2\text{}}$ is well-defined and T is the strong solution of the Monge–Ampère equation ΛL°T=1 a.s. on W. To cite this article: D. Feyel, A.S. Üstünel, C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

Schrödinger Operators with Random Sparse Potentials. Existence of Wave Operators

We consider the connection problem for the Heun differential equation, which is a Fuchsian differential equation that has four regular singular points. We consider the case in which the parameters in this equation satisfy a certain set of conditions coming from the eigenvalue problem of the non-commutative harmonic oscillators. As an application, we describe eigenvalues with multiplicities greater than 1 and the corresponding odd eigenfunctions of the non-commutative harmonic oscillators. The existence of a rational or a certain algebraic solution of the Heun equation implies that the corresponding eigenvalues has multiplicities greater than 1.The research of the author is supported in part by a Grant-in-Aid for Scientific Research (B) (No. 15340005) from the Ministry of Education, Culture, Sports, Science and Technology.Mathematics Subject classifications (2000). primary, 34M35, secondary, 33E20.This revised version was published online in March 2005 with corrections to the cover date.     

Photodynamic inactivation of isolated crayfish neuron requires protein kinase C,PI 3-kinase and Ca2+

Involvement of some signalling pathways in response to photodynamic therapy (PDT) of sulfonated aluminium phthalocyanine Photosens has been studied in isolated nerve cell. Neurone photosensitisation with 10(-7) M Photosens gradually inhibited firing and irreversibly abolished neuronal activity. Activation of protein kinase C (PKC) by phorbol ester 12-O-tetradecanoylphorbol 13-acetate (TPA) precipitated PDT-induced abolition of neurone activity and caused nucleus swelling and impairment of the nucleus border. Elevation of cytosolic Ca(2+) concentration by ionomycin or thapsigargin also reduced neurone lifetime. In contrast, the PKC inhibitors staurosporine, hypericin or chelerythrine as well as the phosphatidylinositol 3-kinase (PI 3-kinase) inhibitors wortmannin or LY294002 increased neurone lifetime. These results showed that PKC, PI 3-kinase and Ca(2+) are involved in PDT-induced neurone inactivation and following death.     

Unprecedented conversion of triethylamine and disulfur dichloride into a thienopentathiepin and a heptathiocane

[reaction: see text] In a remarkable cascade reaction, triethylamine is converted into the thienopentathiepin 2a and the heptathiocane 3a by a preequilibrated solution of disulfur dichloride and DABCO in chloroform.     

Approximation and Prediction of the Numerical Solution of Some Burgers Problems

The Aitken's ²-prediction of Brezinski has already been used by Morandi Cecchi et al. in order to compute a numerical approximation of the solution of a parabolic initial-boundary value problem. This method consists in two consecutive steps: the first one is the approximation with a finite elements method, where the solution of the involved nonlinear system is computed by Gauss–Seidel method; the second one is a prediction of further terms with Aitken's ²-process. By comparison with this method, we use other methods of prediction in another way. First, we consider a generalization of ²-prediction, the so-called -prediction. In this paper, we only use vector prediction which is more stable than the scalar one. Then, the methods of prediction presented can be used in order to predict the starting vector of the Gauss–Seidel method.     

On the Topology of Fibrations with Section and Free Loop Spaces

We relate the brace products of a fibration with section tothe differentials in its Serre spectral sequence. In the particularcase of free loop fibrations, we establish a link between thesedifferentials and Browder operations in the fiber. Applicationsand several calculations (for the particular cases of spheresand wedges of spheres) are given. 2000 Mathematical SubjectClassification: 55P35, 55Q15, 55R05, 55R20.     

Stationary Flow Past a Semi-Infinite Flat Plate: Analytical and Numerical Evidence for a Symmetry-Breaking Solution

We consider the question of the existence of stationary solutions for the Navier Stokes equations describing the flow of a incompressible fluid past a semi-infinite flat plate at zero incidence angle. By using ideas from the theory of dynamical systems we analyze the vorticity equation for this problem and show that a symmetry-breaking term fits naturally into the downstream asymptotic expansion of a solution. Finally, in order to check that our asymptotic expressions can be completed to a symmetry-breaking solution of the Navier–Stokes equations we solve the problem numerically by using our asymptotic results to prescribe artificial boundary conditions for a sequence of truncated domains. The results of these numerical computations a clearly compatible with the existence of such a solution. Mathematics Subject Classification (2000). 76D05, 76D25, 76M10, 41A60, 35Q35 Supported in part by the Fonds National Suisse.     

Packing and covering with linear programming: A survey

This paper considers the polyhedral results and the min–max results on packing and covering problems of the decade. Since the strong perfect graph theorem (published in 2006), the main such results are available for the packing problem, however there are still important polyhedral questions that remain open. For the covering problem, the main questions are still open, although there has been important progress. We survey some of the main results with emphasis on those where linear programming and graph theory come together. They mainly concern the covering of cycles or dicycles in graphs or signed graphs, either with vertices or edges; this includes the multicut and integral multiflow problems.     

Vertex Operator Solutions of¶2d Dimensionally Reduced Gravity

We apply algebraic and vertex operator techniques to solve two dimensional reduced vacuum Einstein's equations. This leads to explicit expressions for the coefficients of metrics solutions of the vacuum equations as ratios of determinants. No quadratures are left. These formulas rely on the identification of dual pairs of vertex operators corresponding to dual metrics related by the Kramer-Neugebauer symmetry.